Consider a system with a time-dependent Hamiltonian. We know that the evolution of the state of this system, is given by ## \displaystyle |\Psi(t_1)\rangle=T \exp\left( -i \int_{t_0}^{t_1} dt H(t) \right) |\Psi(t_0)\rangle ##.(adsbygoogle = window.adsbygoogle || []).push({});

Do you think you can prove that the path integral formula for the state(the one which was the ground state at ## t=-\infty ##) of this system, can be given by the formula below?

##\displaystyle \Psi(x,t)\propto \int_{z(t=-\infty)=const}^{z(t)=x} \mathcal D [z(t)] \ e^{iS[z(t)]} ##

Thanks

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# A Path integral formula for a state with non-trivial time dependency

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